A generalization of the Apostol-type Frobenius–Genocchi polynomials of level ι

Letelier Castilla; Clemente Cesarano; Daniel Bedoya; William Ramírez; Praveen Agarwal; Shilpi Jain

doi:10.1016/B978-0-44-315423-2.00007-2

A generalization of the Apostol-type Frobenius–Genocchi polynomials of level ι

Letelier Castilla
, Clemente Cesarano
, Daniel Bedoya
, William Ramírez
, Praveen Agarwal
, Shilpi Jain

Nonlinear Dynamic Research Centre (NDRC)

I.E.E. Normal Superior Nuestra Señora de Fátima
International Telematic University Uninettuno
Universidad Metropolitana
Universidad de la Costa
International College of Engineering
Poornima College of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

5 Scopus citations

Abstract

The main objective of this paper is to present the generalized Apostol-type Frobenius–Genocchi polynomials and numbers of level ι and order α. We give some basic identities and properties (summation formula, differential and integral relations, addition theorems, and so on) via generating function techniques. Also, we provide certain relationships between these polynomials and the Stirling numbers of the second kind and other polynomial families. Finally, we obtain a differential equation and a recurrence relation for these polynomials.

Original language	English
Title of host publication	Fractional Differential Equations
Subtitle of host publication	Theoretical Aspects and Applications
Publisher	Elsevier
Pages	11-26
Number of pages	16
ISBN (Electronic)	9780443154232
ISBN (Print)	9780443154249
DOIs	https://doi.org/10.1016/B978-0-44-315423-2.00007-2
State	Published - 1 Jan 2024

Keywords

Differential equations
Generalized Apostol-type Frobenius–Genocchi polynomials
Generalized Apostol–Genocchi polynomials
Recurrence relations

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10.1016/B978-0-44-315423-2.00007-2

Cite this

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abstract = "The main objective of this paper is to present the generalized Apostol-type Frobenius–Genocchi polynomials and numbers of level ι and order α. We give some basic identities and properties (summation formula, differential and integral relations, addition theorems, and so on) via generating function techniques. Also, we provide certain relationships between these polynomials and the Stirling numbers of the second kind and other polynomial families. Finally, we obtain a differential equation and a recurrence relation for these polynomials.",

keywords = "Differential equations, Generalized Apostol-type Frobenius–Genocchi polynomials, Generalized Apostol–Genocchi polynomials, Recurrence relations",

author = "Letelier Castilla and Clemente Cesarano and Daniel Bedoya and William Ram{\'i}rez and Praveen Agarwal and Shilpi Jain",

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T1 - A generalization of the Apostol-type Frobenius–Genocchi polynomials of level ι

AU - Castilla, Letelier

AU - Cesarano, Clemente

AU - Bedoya, Daniel

AU - Ramírez, William

AU - Agarwal, Praveen

AU - Jain, Shilpi

PY - 2024/1/1

Y1 - 2024/1/1

N2 - The main objective of this paper is to present the generalized Apostol-type Frobenius–Genocchi polynomials and numbers of level ι and order α. We give some basic identities and properties (summation formula, differential and integral relations, addition theorems, and so on) via generating function techniques. Also, we provide certain relationships between these polynomials and the Stirling numbers of the second kind and other polynomial families. Finally, we obtain a differential equation and a recurrence relation for these polynomials.

AB - The main objective of this paper is to present the generalized Apostol-type Frobenius–Genocchi polynomials and numbers of level ι and order α. We give some basic identities and properties (summation formula, differential and integral relations, addition theorems, and so on) via generating function techniques. Also, we provide certain relationships between these polynomials and the Stirling numbers of the second kind and other polynomial families. Finally, we obtain a differential equation and a recurrence relation for these polynomials.

KW - Differential equations

KW - Generalized Apostol-type Frobenius–Genocchi polynomials

KW - Generalized Apostol–Genocchi polynomials

KW - Recurrence relations

UR - https://www.scopus.com/pages/publications/85199049275

U2 - 10.1016/B978-0-44-315423-2.00007-2

DO - 10.1016/B978-0-44-315423-2.00007-2

M3 - Chapter

AN - SCOPUS:85199049275

SN - 9780443154249

SP - 11

EP - 26

BT - Fractional Differential Equations

PB - Elsevier

ER -

A generalization of the Apostol-type Frobenius–Genocchi polynomials of level ι

Abstract

Keywords

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